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The vector linear program solver Bensolve – notes on theoretical background

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  • Löhne, Andreas
  • Weißing, Benjamin

Abstract

Bensolve is an open source implementation of Benson’s algorithm and its dual variant. Both algorithms compute primal and dual solutions of vector linear programs (VLP), which include the subclass of multiple objective linear programs (MOLP). The recent version of Bensolve can treat arbitrary vector linear programs whose upper image does not contain lines. This article surveys the theoretical background of the implementation. In particular, the role of VLP duality for the implementation is pointed out. Some numerical examples are provided. In contrast to the existing literature we consider a less restrictive class of vector linear programs.

Suggested Citation

  • Löhne, Andreas & Weißing, Benjamin, 2017. "The vector linear program solver Bensolve – notes on theoretical background," European Journal of Operational Research, Elsevier, vol. 260(3), pages 807-813.
    • Handle: RePEc:eee:ejores:v:260:y:2017:i:3:p:807-813
    DOI: 10.1016/j.ejor.2016.02.039
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    1. Lizhen Shao & Matthias Ehrgott, 2008. "Approximately solving multiobjective linear programmes in objective space and an application in radiotherapy treatment planning," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(2), pages 257-276, October.
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    4. Andreas Hamel & Andreas Löhne & Birgit Rudloff, 2014. "Benson type algorithms for linear vector optimization and applications," Journal of Global Optimization, Springer, vol. 59(4), pages 811-836, August.
    5. Dauer, Jerald P. & Liu, Yi-Hsin, 1990. "Solving multiple objective linear programs in objective space," European Journal of Operational Research, Elsevier, vol. 46(3), pages 350-357, June.
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    Cited by:

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    2. Piercy, Craig A. & Steuer, Ralph E., 2019. "Reducing wall-clock time for the computation of all efficient extreme points in multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 277(2), pages 653-666.

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